Repeated Exponentiation
Just as exponentiation of natural numbers is motivated by repeated multiplication, it is possible to define an operation based on repeated exponentiation; this operation is sometimes called tetration. Iterating tetration leads to another operation, and so on. This sequence of operations is expressed by the Ackermann function and Knuth's up-arrow notation. Just as exponentiation grows faster than multiplication, which is faster growing than addition, tetration is faster growing than exponentiation. Evaluated at (3,3), the functions addition, multiplication, exponentiation, tetration yield 6, 9, 27, and 7,625,597,484,987 respectively.
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Famous quotes containing the word repeated:
“Manners are the happy way of doing things; each once a stroke of genius or of love—now repeated and hardened into usage. They form at last a rich varnish, with which the routine of life is washed, and its details adorned. If they are superficial, so are the dewdrops which give such depth to the morning meadows.”
—Ralph Waldo Emerson (1803–1882)